Electrostatic repulsion between two parallel plates covered with polymer brush layers

Abstract

An expression for the electrostatic repulsive force is obtained for two parallel similar plates immersed in an electrolyte solution at separation h covered with a uniformly charged polymer brush layer of intact thickness d _o under compression (h<2d _o) after the two brushes come into contact. It is assumed that when the two brushes come into contact, they are squeezed against each other but do not interdigitate. The electrostatic repulsive force is found to increase with decreasing h as 1/h for highly charged brushes and as 1/h ² for weakly charged brushes. This is in contrast to the interaction force between the brush layers before contact (h≥2d _o), which is essentially proportional to exp[−κ(h−2d _o)] (where κ is the Debye–Hückel parameter). It is also shown that the interaction force for highly charged brushes, which becomes independent of the electrolyte concentration, can be comparable in magnitude to the steric repulsive forces between the brushes resulting from osmotic repulsion and the elastic energy of the brushes.